Physics
(a) How far from a 53.6 mm focal-length lens must an object be placed if its image is to be magnified 2.12X and be real?
(b) What if the image is to be virtual and magnified 2.12X?
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Answers
(a) The object must be placed at a distance of 25.17 mm from the lens. This can be calculated using the lens equation: 1/s + 1/s' = 1/f, where s is the object distance, s' is the image distance, and f is the focal length of the lens. We can rearrange the equation to solve for s: s = f(s' - 1)/s' = 53.6 (2.12 - 1)/2.12 = 25.17. (b) It is impossible for the image to be both virtual and magnified 2.12X. Virtual images are always behind the lens, so the image distance (s') is always negative, which is a solution that is not compatible with a magnification of 2.12X.
